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Study of signal to noise ratio for different order of field amplitude in CARS process

Priyanka Kapil

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This paper investigates the generation of Signal to Noise Ratio (SNR) in Coherent anti-Stokes Raman Scattering (CARS) process in various orders of field amplitude for a squeezed light. Furthermore, we show that the signal-to-noise ratio is enhanced at lower orders of the field amplitude and scales proportionally with the number of pump photons present in the nonlinear medium before the interaction.

DOI
10.1051/epjconf/202637501003

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Study of signal to noise ratio for different order of field amplitude in CARS process

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Optics Letters•Jun 1, 1988•14 citations
This paper investigates the generation of Signal to Noise Ratio (SNR) in Coherent anti-Stokes Raman Scattering (CARS) process in various orders of field amplitude for a squeezed light. Furthermore, we show that the signal-to-noise ratio is enhanced at lower orders of the field amplitude and scales proportionally with the number of pump photons present in the nonlinear medium before the interaction.
The non-classical effects of squeezing of light in coherent anti-Stokes Raman scattering (CARS) and coherent anti-Stokes hyper-Raman scattering (CAHRS) are investigated under the short-time approximation based on a fully quantum mechanical approach. In an idealized model CARS, the interaction is looked upon as a process involving absorption of a pump photon and emission of a Stokes photon, which is followed by absorption of a pump photon and subsequently emission of an anti-Stokes photon at a different frequency, whereas CAHRS is looked upon as a process involving absorption of two pump photons and emission of a Stokes photon, which is followed by absorption of two more pump photons and subsequent emission of an anti-Stokes photon at a different frequency. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. It is shown that squeezing in the Stokes and anti-Stokes mode in CARS is found to be dependent on amplitude-squared squeezing of the initial pump field while, in CAHRS, it is dependent on the fourth-order amplitude squeezing of the initial pump field. Higher-order squeezing can be converted to linear squeezing through these processes. It is also shown that squeezing is greater in CAHRS than the corresponding squeezing in CARS.
Coherent anti-Stokes Raman scattering (CARS) is a well-known Raman scattering process that occurs when Stokes, anti-Stokes and pump waves are properly phase-matched. Using a quantum-field approach with Langevin noise sources, we calculate the noise figure for wavelength conversion between the Stokes and anti-Stokes waves in CARS and show its dependence on phase mismatch. Under phase matched conditions, the minimum noise figure is approximately 3 dB, with a correction that depends on the pump frequency, Stokes shift, refractive indices, and nonlinear susceptibilities. We calculate the photon statistics of CARS and show that the photon number distribution is non-Gaussian. Our findings may be significant for currently pursued applications of CARS including wavelength conversion in data transmission and spectroscopic detection of dilute biochemical species.
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.
The degree of phase cross correlation between a fluctuating pump wave and the Stokes wave, which is generated by stimulated Raman scattering, can be determined by observing the spectrum of anti-Stokes light generated by coherent anti-Stokes Raman scattering (CARS). The spectrum of the anti-Stokes light has two distinct features: one that arises from scattering through an off-resonant virtual level and one that arises from resonant scattering through the real level. This provides a method to measure the phase cross correlation between two optical fields of different color. The intensity of the anti-Stokes signal strongly depends on the degree of cross correlation. Depending on the detuning from Raman resonance in the CARS process, the anti-Stokes intensity can be either enhanced or suppressed with respect to the case of uncorrelated fields.1